Enhanced Electron Correlation and Significantly Suppressed Thermal Conductivity in Dirac Nodal‐Line Metal Nanowires by Chemical Doping

Abstract Enhancing electron correlation in a weakly interacting topological system has great potential to promote correlated topological states of matter with extraordinary quantum properties. Here, the enhancement of electron correlation in a prototypical topological metal, namely iridium dioxide (IrO2), via doping with 3d transition metal vanadium is demonstrated. Single‐crystalline vanadium‐doped IrO2 nanowires are synthesized through chemical vapor deposition where the nanowire yield and morphology are improved by creating rough surfaces on substrates. Vanadium doping leads to a dramatic decrease in Raman intensity without notable peak broadening, signifying the enhancement of electron correlation. The enhanced electron correlation is further evidenced by transport studies where the electrical resistivity is greatly increased and follows an unusual T dependence on the temperature (T). The lattice thermal conductivity is suppressed by an order of magnitude via doping even at room temperature where phonon‐impurity scattering becomes less important. Density functional theory calculations suggest that the remarkable reduction of thermal conductivity arises from the complex phonon dispersion and reduced energy gap between phonon branches, which greatly enhances phase space for phonon–phonon Umklapp scattering. This work demonstrates a unique system combining 3d and 5d transition metals in isostructural materials to enrich the system with various types of interactions.


Synthesizing V-doped IrO2 (Ir1-xVxO2) nanowires using a three-zone quartz tube furnace
Ir1-xVxO2 nanowires were synthesized in a three-zone quartz tube furnace via a chemical vapor deposition (CVD) process [ Figure S1]. Vanadium oxide (VO2) powder (Aldrich, ≥99% trace metals basis) and iridium oxide (IrO2) powder (Alfa Aesar, 99.99% metals basis) were placed in alumina boats in the center of zones 1 and 2, respectively, and silicon substrates were placed in the downstream zone 3. Prior to the growth, the Si substrates were scratched with a diamond tip pen to create a fresh and rough surface. Figure S1. A schematic of the three-zone quartz tube furnace used to grow Ir1-xVxO2 nanowires.

Density contrast of nanowires varies with the depth of the scratches and the soaking time
As shown in Figure S2, the contrast in the density of nanowires in the scratched versus unscratched regions becomes less dramatic with an increase in growth duration. A longer growth time may lead to more nucleation occurring and thus more nanowires are grown on the flat regions of the substrate. Additionally, the depth of the scratches has an impact on the density of nanowires grown on the substrates. In the order of the deepest to shallowest scratches: Figure   S2  was used during the growths, respectively. We note that the scratches in the 120 min growth were the deepest between the three growths. The dashed X in (c) is used as a guide to the eye to indicate the shallow scratches on the substrate.

Tapered morphology of nanowires outside of the scratches
On the unscratched regions of the growth substrates, the diffused atoms wet on the flat substrate and are more inclined to grow along the substrate and are typically partially embedded in the substrate, leading to a more tapered-looking morphology, as shown in Figure S3.

TEM-XEDS measurements of oxygen with a single detector versus dual detectors
The TEM-XEDS oxygen mapping of a doped IrO2 nanowire measured with a single detector appears asymmetric across its diameter [ Figure S4], however, this effect is due to the absorption effect when only one detector is positioned asymmetrically from the nanowire (e.g., to the left or right of the nanowire). This result can be corrected with a measurement using a dual-detector system, as shown in Figure S5, where the oxygen mapping is shown to be symmetric.

XEDS
The V concentration of the nanowires in the Raman measurements (x = + ) were measured through SEM-XEDS. As shown in Figure S6, the nanowire has ~16% V, where we estimate the error to be within a few percent for this semi-quantitative tool. Figure S6. A SEM image and XEDS spectrum of a representative nanowire.

Raman measurements and peak fittings on nanowires of various V concentrations
A laser power of 50 μW was used for all Raman measurements and all of the nanowires measured were of similar diameters (~320 nm). The Raman peaks for each spectrum were fitted [ Figure S7] using IGOR Pro 6.37's built in multi-peak fitting package which provides quantities for the amplitude, area intensity, FWHM, etc. and their respective errors. Figure S7. A fitting of the 520 cm -1 (Si substrate) and ~560 cm -1 peaks in the spectra of a representative Ir1-xVxO2 nanowire in the range between ~465 and 615 cm -1 .

Measuring the V concentration of nanowires via TEM-XEDS
After the transport measurements, we transferred the same nanowires to a TEM grid and performed TEM-XEDS on three different regions of each nanowire (near each of the ends and a region in the middle) and averaged them to determine their respective V concentrations (x), as shown in Figure S8. The average x values for the nanowires of various diameters are shown in Table S1.  Table S1. The diameter and respective averaged x values determined from TEM-XEDS.

The electronic density of states of IrO2 and V0.25Ir0.75O2
The electronic density of states for IrO2 and Ir0.75V0.25O2 were calculated using density functional theory, as shown in the top and bottom panels of Figure S9, respectively.

The Analysis of electrical transport data using thermal activation model
The expression for electrical resistivity resulting from activation across a bandgap, such as in semiconductors, is written as: = 2 , where is the bandgap and is the Boltzmann constant. If it is thermal activation which leads to the non-metallic behavior, ln would be proportional to −1 , which is not the case for our samples [ Figure S10].

Analysis of electrical transport data using Anderson localization
The behavior of resistivity caused by Anderson (strong) localization is described by the variable range hopping (VRH) model: , where is the dimensionality. By fitting the data in the low temperature regime, we can find 0 and the localization length can be computed using 0 = 16 ⋅ ( )⋅ 3 , [1] where the density of states at the Fermi energy ( ) can be determined from Figure S9. Figure S12 shows the fitting of the 87 nm and 139 nm nanowires when = 3. The fitting parameters and determined localization lengths for all dimensionalities are displayed in Table S2. The 139 nm nanowire is expected to have the smallest localization length since it has the largest change of resistivity, however, its localization length is still much larger than the size of unit cell. As for the other nanowires, are found to be hundreds of times the size of the unit cell. Therefore, it is unlikely that Anderson localization plays an important role in the behavior of resistivity.

Magnetoresistance (MR)
Magnetoresistance data were taken at temperatures between 20-200 K and 5-15 K while sweeping the field from -6.5 T to 6.5 T and from -1 T to 1 T, respectively, as shown in Figure   S13.
is the diffusion constant and can be computed using = While the data on the 139 nm nanowire shows some deviations from the predicted value, the 108 nm and 87 nm nanowires agree with the prediction, both showing increases less than the possible largest value. Hence the direct EEI effect cannot readily be excluded as a viable explanation.

Estimation of mean free path and electron-phonon scattering rate
To estimate the mean free path, we use the equation = which is of the same order, but smaller, than the (10 ) = 2.5 − 3.7 nm of IrO2 calculated in the literature due to the doping enhanced scattering and higher temperature. [2] Electron-phonon (e-ph) scattering usually reveals itself by showing a ∝ 5 behavior at low temperatures. However, this temperature dependence is not observed in our system because of the weaker contribution of electron-phonon scattering in comparison to the other mechanisms discussed in our paper. The absence of this dependence makes it difficult to extract information about e-ph scattering directly from the electrical transport data. On the other hand, since we observed a clear size effect in lattice thermal conductivity, a rough estimation is that the e-ph scattering rate is comparable to or weaker than the boundary scattering. Our DFT calculations of phonon dispersion suggests that the acoustic phonon group velocity is on the order of kilometers per second, and the nanowires are around 100 nm wide. We then roughly estimate the rate of phonon-boundary scattering rate to be ℎ− −1 ≈~10 10 s −1 and the electron-phonon scattering rate to be − ℎ −1 ≤ 10 10 s −1 . Combined with the Fermi velocity, we estimate that the characteristic length scale of e-ph scattering is on the order of a micron, which is much larger than the electron mean free path, indicating the contribution of e-ph scattering to the charge transport is indeed negligible in our system.

Contact thermal resistance after wetting and EBID treatment is negligible
The effect of the contact thermal resistance was estimated by measuring the same nanowire with different contact treatments. As shown in Figure S15, the measured thermal conductance increases after the wetting treatment and the first round of EBID but remains essentially the same after a second round of EBID. As such, the contact thermal resistance after wetting and EBID treatment can be regarded as negligible.